اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMotivic homotopy theory of group scheme actions
500
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish homotopical purity and blow-up theorems for finite abelian groups.
قيم البحث
اقرأ أيضاً
For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that after comp
leting at a prime and eta (the motivic Hopf map) this results in a full and faithful embedding whenever k is real closed and L = k[i]. It is a full and faithful embedding after eta-completion if a motivic version of Serres finiteness theorem is valid. We produce strong necessary conditions on the field extension L/k for this functor to be full and faithful. Along the way, we produce several results on the stable C_2-equivariant Betti realization functor and prove convergence theorems for the p-primary C_2-equivariant Adams spectral sequence.
We determine systematic regions in which the bigraded homotopy sheaves of the motivic sphere spectrum vanish.
Let F be a field of characteristic different than 2. We establish surjectivity of Balmers comparison map rho^* from the tensor triangular spectrum of the homotopy category of compact motivic spectra to the homogeneous Zariski spectrum of Milnor-Witt
K-theory. We also comment on the tensor triangular geometry of compact cellular motivic spectra, producing in particular novel field spectra in this category. We conclude with a list of questions about the structure of the tensor triangular spectrum of the stable motivic homotopy category.
For each prime $p$, we define a $t$-structure on the category $widehat{S^{0,0}}/tautext{-}mathbf{Mod}_{harm}^b$ of harmonic $mathbb{C}$-motivic left module spectra over $widehat{S^{0,0}}/tau$, whose MGL-homology has bounded Chow-Novikov degree, such
that its heart is equivalent to the abelian category of $p$-completed $BP_*BP$-comodules that are concentrated in even degrees. We prove that $widehat{S^{0,0}}/tautext{-}mathbf{Mod}_{harm}^b$ is equivalent to $mathcal{D}^b({{BP}_*{BP}text{-}mathbf{Comod}}^{{ev}})$ as stable $infty$-categories equipped with $t$-structures. As an application, for each prime $p$, we prove that the motivic Adams spectral sequence for $widehat{S^{0,0}}/tau$, which converges to the motivic homotopy groups of $widehat{S^{0,0}}/tau$, is isomorphic to the algebraic Novikov spectral sequence, which converges to the classical Adams-Novikov $E_2$-page for the sphere spectrum $widehat{S^0}$. This isomorphism of spectral sequences allows Isaksen and the second and third authors to compute the stable homotopy groups of spheres at least to the 90-stem, with ongoing computations into even higher dimensions.
We survey computations of stable motivic homotopy groups over various fields. The main tools are the motivic Adams spectral sequence, the motivic Adams-Novikov spectral sequence, and the effective slice spectral sequence. We state some projects for future study.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
